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I have multiple datasets in my ArcGIS, each having different map projections. All of them are vectors. Some are using Sphere Mercator, others using WGS84. I cannot perform the reprojection function in ArcGIS as I do not have the formula for geographic transformation. I am stuck and cannot proceed to make a map due to this issue.

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The problem is almost certainly with the "Sphere_Mercator" data. This projected coordinate reference system (CRS) is using a sphere-based geographic CRS. ArcGIS doesn't have any predefined geographic/datum transformations that convert to or from a sphere.

The data may have been built on the sphere, or it might have been built on WGS 1984 and then projected to the Sphere_Mercator CRS.

If you have reference data in WGS 1984 that you can compare the Sphere_Mercator data to, add both to ArcMap. Set the data frame to use the WGS 1984-based CRS. Does the Sphere_Mercator line up correctly? If so, unproject it to "Sphere" GeoCRS using the Project Tool, then use the Define Projection tool to change the CRS to WGS 1984. Then use the Project Tool to convert it to EPSG:3857.

If it doesn't line up, try adding a transformation in ArcMap.

1. Open data frame properties Click the Transformations tab on the
Coordinate System tab. 
2. In the top box, select "GCS_Sphere". The "Into:" box should list WGS 1984. 
3. Click the New button. In the new dialog, set the transformation method to Geocentric_Translations. Leave the transformation parameters set to zeroes.  
4. OK all dialogs and see if the data lines up better. 
5. If it does, right click the layer and select Data, Export Data. Write out a new dataset using the data frame's coordinate reference system.

Disclosure: I work for Esri.

  • up-voted for your thoroughness, but could you please resolve this with the quote I added from the ESRI tech article? If its untrue or misleading, i'll gladly remove it. – Clickinaway Aug 11 '14 at 18:38
  • @Clickinaway Sure! The article is trying to state that if your data is using WGS 1984 as its GeoCRS (and projected or not), no geographic/datum transformation is needed to go to EPSG:3857 because it's also based on WGS 1984. The OP has data that's using "Sphere" as its GeoCRS, not WGS 1984, so ArcGIS wants a transformation. – mkennedy Aug 11 '14 at 18:41
  • Thanks for the clarity; I deleted my answer but if you feel there are any valuable tech articles to accompany your answer please add to your answer. – Clickinaway Aug 11 '14 at 18:51
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If you just want a reprojected dataset, the following libraries/Tools may help:

  • proj4 (C++ library) provide transformation between different projections.
  • GDAL/OGR (C++ library) provide transformation between different vector/raster format, support projection transformation if you specify compiling parameter forcing to compile with proj4 dependency.
  • ogr2ogr : A command line utility in your gdal/ogr installation, you can specify source dataset and projectin(spatial reference system), target dataset and projection type. support different file formats and databases.
  • osm2pgsql : A OpenStreetMap tools that can load osm format vector data into postgresql supporting projection transformation.
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    I don't see any reason to inject an additional application into this as ArcGIS is capable of handling the reprojection process. If Danesh wants to explore scripting the process we can address that as well. – Clickinaway Aug 11 '14 at 13:03

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